1. Field of the Invention
The present invention is in the field of telecommunications and, in particular, in the field of channel estimation in a multiple input scenario, in which a receiver receives signals from more than one transmitting antennas.
2. Description of the Related Art
The steadily-increasing demand for high data rates necessary for today's and future mobile radio applications require high data rate techniques efficiently exploiting the available band width or, in other words, the achievable channel capacity. Therefore, multiple input multiple output (MIMO) transmission systems have achieved considerable importance in recent years. MIMO systems employ a plurality of transmitting points, each of the transmitting points having a transmit antenna, and a plurality of receiving points, each of the receiving points having a receiving antenna, to receive signals being transmitted by the multiple transmitting points through different communication channels. In MIMO techniques, where the signals impinging from several transmitter antennas need to be separated, space-time codes or special multiplexing methods are used.
The signals impinging on each receive antenna are the super-position of the signals from NT antennas, where NT denotes a number of transmitting points. This implies new challenges for channel estimation. Channel parameters, like a channel impulse response or a channel transfer function are required for subsequent processing of the received data. While the separation of the signals corresponding to several transmitting points, each of them having a transmit antenna, is a challenging task, the extension from a receiver having one antenna to a system with several receive antennas is straight forward, as long as the signals are mutually uncorrelated. The structure of the channel estimation units is independent of the number of receive antennas NR. The extension from a multiple input single output (MISO) system to a MIMO system is to employ NR parallel channel estimation units, one for each receiving point (receive antenna).
The use of coherent transmission techniques in wireless systems requires estimation and tracking of the mobile radio channel. Since the signals transmitted from multiple transmit antennas are observed as mutual interference, channel estimation for MIMO systems is different from the single transmit antenna scenario. MIMO systems can be used with a multi-carrier modulation scheme to further improve the communication capacity and quality of mobile radio systems. A prominent representative of multi-carrier modulation techniques is the orthogonal frequency division multiplexing (OFDM) technique. A block diagram of an OFDM system is shown in FIG. 7.
Multi carrier modulation in particular orthogonal frequency division multiplexing (OFDM) has been successfully applied to a wide variety of digital communication systems over the past several years. In particular for the transmission of large data rates in a broadcasting scenario (e.g. digital TV), OFDM's superior performance in transmission over dispersive channels is a major advantage. OFDM has been chosen for various digital broadcasting standards, e.g. DAB or DVB-T. Another wireless application of OFDM is in high speed wireless local area networks (WLAN). OFDM was first introduced in the 1960s. An efficient demodulation utilising the discrete Fourier transform (DFT) was suggested by S. Weinstein and P. Ebert, “Data Transmission by Frequency Division Multiplexing Using the Discrete Fourier Transform”, IEEE Transactions on Communication Technology, vol. COM-19, pp. 628-634, October 1971. By inserting a cyclic prefix into the guard interval (GI) longer than the maximum delay of the channel, inter-symbol interference (ISI) can be eliminated completely and the orthogonality of the received signal is preserved. Since future mobile communication systems should support data rates several times higher than current systems, multi-carrier systems with proper coding and interleaving offer both efficient implementation through the application of the Fast Fourier Transform (FFT) and sufficient robustness to radio channel impairments.
Another OFDM-based approach, termed multi-carrier code division multiplex access (MC-CDMA), were spreading in frequency direction as has been introduced in addition to the OFDM modulation, as described in K. Fazel and L. Papke, “On the Performance of Convolutionally-Coded CDMA/OFDM for Mobile Communication Systems”, in Proc. IEEE Int. Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'93), Yokohama, Japan, pp. 468-472, September 1993. MC-CDMA has been deemed to be a promising candidate for the downlink of fourth generation systems. Moreover, a MC/CDMA system with a variable spreading factor has been proposed as described in H. Atarashi and M. Sawahashi, “Variable Spreading Factor Orthogonal Frequency and Code Division Multiplexing (VSF-OFCDM)”, in 3rd International Workshop on Multi-Carrier Spread-Spectrum & Related Topics (MC-SS 2001), Oberpfaffenhofen, Germany, September 2001.
For OFDM-based MIMO systems, one OFDM modulator is employed on each transmitting point, while OFDM demodulation is performed independently for each receiving point. For OFDM, the signal stream is divided into NC parallel sub-streams. The ith sub-stream commonly termed ith sub-carrier of the lth symbol block (OFDM symbol) is denoted by Xl,i. After serial to parallel conversion (S/P) performed by a S/P converter 701 an inverse discrete Fourier transform (DFT) with NFFT points is performed by an IFFT transformer 703 on each block and, subsequently, the guard interval (GI) having NGI samples is inserted by a GI block 705 to obtain a signal xl,n after parallel to serial (P/S) conversion performed by a P/S converter 703. After digital to analogue (D/A) conversion, the signal x(t) is transmitted over a mobile radio channel with an impulse response h(t, .τ). The received signal at receive antenna ν consists of superimposed signals from NT transmitting points. Assuming perfect synchronisation, the received signal impinging at receive antenna ν at sampling instants t=[n+lNsym]Tspl is obtained
      y          l      ,      n              (      v      )        ⁢      =    Δ    ⁢                    y                  (          v          )                    ⁡              (                              [                          n              +                              lN                sym                                      ]                    ⁢                      T            spl                          )              =                                        ∑                          μ              =              1                                      N              T                                ⁢                                          ⁢                                    ∫                              -                ∞                            ∞                        ⁢                                                                                h                                          (                                              μ                        ,                        v                                            )                                                        ⁡                                      (                                          t                      ,                      τ                                        )                                                  ·                                                      x                                          (                      μ                      )                                                        ⁡                                      (                                          t                      -                      τ                                        )                                                              ⁢                                                          ⁢                              ⅆ                τ                                                    +                  n          ⁡                      (            t            )                              ⁢              |                  t          =                                    [                              n                +                                  lN                  sym                                            ]                        ⁢                          T              spl                                          where n(t) represents additive white Gaussian noise, and Nsym=NFFT+NGI accounts for the number of samples per OFDM symbol. The * operator denotes convolution. The signal yl,n received by the receiver is first serial to parallel (S/P) converted by a S/P converter 709 and the guard interval is removed by a GI block 711. The information is recovered by performing a discrete Fourier transform (DFT) on the received block of signal samples (in FIG. 7 a FFT transformer 713 is used) to obtain the output of the OFDM demodulation Yl,I in the frequency domain. The received signal at receive antenna ν after OFDM demodulation is given by
      Y          l      ,      i              (      v      )        =                    ∑                  μ          =          1                          N          T                    ⁢                          ⁢                        X                      l            ,            i                                (            μ            )                          ·                  H                      l            ,            i                                (                          μ              ,              v                        )                                +          N              l        ,        i            where Xl,i(μ) and Hl,i(μ,ν) denotes the transmitted information symbol and the channel transfer function (CTF) of transmit antenna μ, at sub-carrier i of the lth OFDM symbol, respectively. The term Nl,i accounts for additive white Gaussian noise (AWGN) with zero mean and variance No.
When transmitting an OFDM signal over a multi-path fading channel, the received signal will have unknown amplitude and phase variations. For coherent transmission, these amplitude and phase variations need to be estimated by a channel estimator.
In the following, reference is made to pilot symbol-aided channel estimation (PACE), where a sub-set of the transmitted data is reserved for transmitting known information, termed “pilot symbols”. These pilots are used as side information for channel estimation.
To formally describe the problem, the received pilot of OFDM symbol lDt at the (iDf)th sub-carrier
                                          Y                                                            l                  ~                                ⁢                                  D                  t                                            ,                                                i                  ~                                ⁢                                  D                  f                                                              =                                                    ∑                                  μ                  =                  1                                                  N                  T                                            ⁢                                                          ⁢                                                X                                                                                    l                        ~                                            ⁢                                              D                        t                                                              ,                                                                  i                        ~                                            ⁢                                              D                        f                                                                                                  (                    μ                    )                                                  ⁢                                  H                                                                                    l                        ~                                            ⁢                                              D                        t                                                              ,                                                                  i                        ~                                            ⁢                                              D                        f                                                                                                  (                    μ                    )                                                                        +                          N                                                                    l                    ~                                    ⁢                                      D                    t                                                  ,                                                      i                    ~                                    ⁢                                      D                    f                                                                                      ⁢                                                                l          ~                =                  {                      1            ,            2            ,            ⋯            ⁢                                                  ,                          L              /                              D                t                                              }                                                                              i          ~                =                  {                      1            ,            2            ,            ⋯            ⁢                                                  ,                                          N                c                            /                              D                f                                              }                    where X{tilde over (l)}Dt,ĩDf(μ) and H{tilde over (l)}Dt,ĩDf(μ,ν) denotes the transmitted pilot symbol and the channel transfer function (CTF) of transmit antenna μ, at sub-carrier i=ĩDf of the l={tilde over (l)}Dtth OFDM symbol, respectively. It is assumed that the CTF varies in the l and in the i variable, i.e. in time and in frequency. The term N{tilde over (l)}Dt,ĩDf accounts for additive white Gaussion noise. Furthermore, l represents the number of OFDM symbols per frame, Nc is the number of sub-carriers per OFDM symbol, Df and Dt denote the pilot spacing in frequency and time, and NT is the number of transmit antennas. The goal is to estimate Hl,i(μ) for all {l,i,μ} within the frame Yl,i is measured. Additionally, the symbols Xl,i(μ) at the location (l,i)=({tilde over (l)}Dt,ĩDf) are known at the receiver. The channel estimation now includes several tasks:    1. The separation of NT superimposed signals,    2. Interpolation in case that Dt or Df are larger than one, and    3. Averaging over the noise N{tilde over (l)}Dt,ĩDf by means of exploiting the correlation of H{tilde over (l)}Dt,ĩDf(μ,ν).
In order to estimate Hl,i(μ) given Y{tilde over (l)}Dt,ĩDf, there are Nc equations with NcNT unknowns, when one OFDM symbol is considered. Thus, a straight-forward solution of this linear equation system does, in general, not exist. By transforming Y{tilde over (l)}Dt,ĩDf to the time domain, the number of unknowns can be reduced, making it possible to solve the resulting equation system in the time domain. This approach has the advantage that DFT-based interpolation, which is a standard technique, can be combined with estimation and separation of NT superimposed signals in one step, resulting in a computationally efficient estimator.
For time domain channel estimation for MIMO-OFDM systems, the received pilots of one OFDM symbol Y{tilde over (l)}Dt,ĩDf are pre-multiplied by the complex conjugate of the transmitted pilot sequence X{tilde over (l)}Dt,ĩDf*, for 1≦ĩ≦N′P. Then the result is transformed into the time domain via an N′p-point IDFT. Subsequently, the NT superimposed signals are separated by a matrix inversion. The time domain channel estimate is obtained by filtering the output of the IDFT operation with a finite impulse response (FIR) filter. The DFT-based interpolation is performed simply by adding Nc-Q zeros for the channel impulse response (CIR) estimates, i.e. to extend the length of the estimate of length Q to Nc samples. This technique is called of zero padding. An N′p-point DFT transforms the CIR estimate of the pilots to the frequency response estimate of the entire OFDM symbol.
Estimators based on discrete Fourier transform (DFT) have the advantage that a computationally efficient transform in the form of the Fourier transform does exist and that DFT based interpolation is simple.
The performance of the estimation in general is dependent on the choice of the pilot symbols. It is desirable to chose a set of pilot sequences, which minimises the minimum mean squared error (MMSE) criterium (which is a measure of the performance) and the computational complexity of the estimator. Estimators based on the least squares (LS) and the MMSE criterium for OFDM-MIMO systems have been systematically derived by Y. Gong and K. Letaief in: “Low Rank Channel Estimation for Space-Time Coded Wideband OFDM Systems,” in Proc. IEEE Vehicular Technology Conference (VTC'2001-Fall), Atlantic City, USA, pp. 722-776, 2001.
I. Barhumi et al describe in: “Optimal training sequences for channel estimation in MIMO OFDM systems immobile wireless channels”, International Zurich Seminar on Broadband Communications (IZS02), February, 2002 a channel estimation and tracking scheme for MIMO OFDM systems based on pilot tones. In particular, the authors describe a channel estimation scheme based on pilot tones being orthogonal and phase-shifted to each other. Although the pilot symbols described in the above-cited prior art allow an accurate channel estimation, an enormous computational complexity at the receiver is required in order to perform matrix inversions required by the channel estimation algorithm. Due to this high computational complexity, the estimation scheme described in the above prior art document cannot be implemented at low cost, so that the disclosed algorithm may not be suitable for mass-market mobile receivers.
Y. Li, et (“Simplified Channel Estimation for OFDM Systems with Multiple Transmit Antennas,” IEEE Transactions on Wireless Communications, vol. 1, pp. 67-75, January 2002), proposed a channel estimation scheme for OFDM with multiple transmit antennas which is based on the DFT transform. In particular, Li discloses a method for generating pilot symbols to be transmitted by multiple transmit and receive antennas and to be exploited at the receiver for channel estimation. These pilot symbols are generated by multiplying a training sequence having good timing and frequency synchronisation properties by a complex sequence introducing an additional phase shift between the pilot symbols and between the subsequent values of each pilot symbol, as well. To be more specific, each value of a training sequence is multiplied by a complex factor, which introduces a phase shift, wherein the phase shift is dependent of a number being assigned to the value being multiplied, on a number assigned to the corresponding transmitting point and a total number of transmitting points. The pilot symbols are orthogonal and phase shifted to each other. The pilot symbols are modulated by an OFDM scheme and transmitted through a plurality of communication channels. At a receiver, which is one of a plurality of receivers, a signal being received includes a super-position of the plurality of transmitted signals through the plurality of communication channels. Li et al presented further a design rule for the pilot tones based on phase-shifted sequences which is optimum in the mean squared error (MSE) sense. Moreover, a matrix inversion, which is, in general, required for the estimator, can be avoided by choosing orthogonal pilot sequences. However, due to a difficulty of obtaining perfect orthogonality between training sequences, matrix inversions may be necessary.
FIG. 8 shows prior art channel estimation scheme as taught by Li, where the case of two transmitting antennas is considered.
The prior art channel estimator includes a plurality of multipliers, wherein FIG. 8 shows only three multipliers being associated with the kth value of a nth received sequence r[n,k]. A first multiplier 901, a second multiplier 903 and a third multiplier 905 arranged in parallel include first and second inputs and outputs, respectively. The output of the first multiplier 901 is connected to a first inverse fast Fourier transform (IFFT) block 907, the output of the second multiplier 903 is connected to a second IFFT block 909 and the output of the third multiplier 905 is connected to the third IFFT block 911. It should be mentioned here that in total, K multipliers are connected to each IFFT block, wherein K denotes a length of a received sequence in the frequency domain, and a total number of 3K input signals are provided to the three IFFT blocks. Each of the IFFT blocks 907, 909 and 911 is operative to perform an inverse fast Fourier algorithm applied to K input values, respectively. Furthermore, each of the IFFT blocks 907, 909 and 911 includes a number of outputs, wherein only the first K0 outputs of each IFFT block are used. The respective remaining outputs are, for example, connected to ground.
K0 outputs of the first IFFT block 907 are connected to a first estimation block 913 and the first K0 outputs of the third IFFT block 911 are connected to a second estimation block 915. The K0 outputs of the second IFFT block 909 are connected to the first estimation block 913 and to the second estimation block 915, respectively. The first estimation block 913 and the second estimation block 915 have K0 outputs, each of the outputs being connected to a corresponding filter 917 of a plurality of filters, each of the filters having an output, respectively. The K0 outputs of the filters 917 corresponding to the first estimation block 913 are connected to a first Fourier transform (FFT) block 917 and the K0 outputs of the filter 917 corresponding to the second estimation block 915 are connected to a second FFT block 921. The first FFT block 919 and the second FFT block 921 have K outputs, where K is, as stated above, the number of sub-carriers. Furthermore, due to the simplified algorithm described by Li, the outputs of the first filters 917 corresponding to the first estimation block 913 are connected to the second estimation block 915 and the outputs of the filter 917 corresponding to the second estimation block 915 are further connected to the first estimation block 913, so that a plurality of feedback loops is established.
As stated above, FIG. 8 shows an example of the prior art estimator for the case of two transmit antennas, so that the received signal r[n,k] is a superposition of two transmitted signals being possibly corrupted by channel noise. The received signal is split into two received signals by a splitting means not shown in FIG. 8. The copies of the received signals are then multiplied by complex conjugated signals corresponding to the respective transmit antennas. Moreover, the pilot symbol transmitted by the first transmit antenna is multiplied by a complex conjugated version of the pilot symbol transmitted by the second antenna. More precisely, the K values of the first copy of the received signal are multiplied by K values of the complex conjugated version of the pilot symbol transmitted by the first antenna. The K values of the second version of the received signal is multiplied by K values of the complex conjugated version of the pilot symbol transmitted by the second transmit antenna. Furthermore, the K values of the pilot symbol transmitted by the first antenna is multiplied by K complex conjugated values of the pilot symbol transmitted by the second transmit antenna in order to obtain intermediate values required by the subsequent channel estimation algorithm.
As stated above, all multiplications are performed in parallel, so that the K results from the multipliers 901 are fed to the first IFFT block 907. K results from the K multipliers 903 are fed to the second IFFT block 909. K results from the K multipliers 905 are fed to the third IFFT block 911. Each respective IFFT block is operative to perform an inverse fast Fourier transform in order to transform the frequency domain input signals into time domain output signals.
The first and the second estimation block, 913 and 915, are operative to perform a channel estimation algorithm based on the plurality of the input signals. More precisely, the first estimation block 913 receives 3K0 input signals to generate K0 output signals corresponding to the channel impulse response of the first channel from the first transmit antenna to the considered receive antenna. The second estimation block 915 receives, in an analogue way, 3K0 input signals to generate K0 output values corresponding to the second communication channel from the second transmit antenna to the receive antenna. The respective K0 output values are then filtered by filters 917.
As stated above, the respective output signals from the filters are fed back to the first and second channel estimation blocks 913 and 915, since the channel estimation blocks 913 and 915 are operative to estimate the channel impulse response of the respective communication channels based on previously-calculated values and on current values obtained from the IFFT blocks. Each estimation block applies an estimation algorithm where matrix by vector multiplications instead of matrix inversions are performed in order to calculate desired channel impulse responses. After filtering and zero padding to a length required by the following fast Fourier transform, a channel transfer function of the first and of the second communication channels are obtained.
As stated above, Li avoids matrix inversions by introducing an iterative scheme where matrix by vector multiplications appear and by exploiting the orthogonality of the pilot symbols. However, in order to calculate two channel impulse responses corresponding to the two communication channels, three inverse fast Fourier transforms, a splitting means and 3K multipliers are required. Moreover, the channel estimation algorithm applied by Li has still a high complexity due to the required matrix by vector multiplications. Hence, with an increasing number of transmit antennas, the complexity of the complicated estimation scheme proposed by Li rapidly increases due to the high number of complex valued multiplications. In addition, the multiplication of the two pilot symbols followed by an inverse Fourier transform is necessary in order to provide a plurality of intermediate values required for channel estimation. Hence, the estimation blocks 913 and 915 cannot operate independently, so that additional timing and control operations are necessary.